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\footnotesize
\noindent Statistica Sinica {\bf 17}(2007), 735-748

\vspace{3pc} \normalsize
\centerline{\large\bf TESTING DYNAMIC RULES OF ANIMAL COGNITIVE}
\vspace{2pt}
\centerline{\large\bf PROCESSING WITH LONGITUDINAL}
\vspace{2pt}
\centerline{\large\bf DISTRIBUTION DATA}
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\author{Fushing Hsieh$^{1,3}$, Shwu-Bin Horng$^2$, Hui-Ying Lin$^3$ and Yen-Chiu Lan$^3$}
\vspace{.4cm} \centerline{\it $^1$University of California at Davis,
$^2$National Taiwan University} \vspace{2pt} \centerline{\it  and
$^3$Academia Sinica} \vspace{.55cm}
\begin{quotation}
\noindent {\it Abstract:}
Identifying the cognitive capacity used by an animal to resolve its foraging
task when facing ever-changing environmental conditions is a recent, central
issue in behavioral ecology and cognitive science. Statistical confirmation
of potential capacity through analysis of individual behavioral processes
becomes an important research topic. New longitudinal data arisec as a
sequence of global quality distributions, representing sparsely observed
environmental dynamics. Such dynamics result from an individual animal's
decision-making process as it explores a patch that consists of a fixed
amount of hosts. Three dynamic rules having distinct degrees of cognitive
capacities are analyzed under a time-varying Markov structure.
From the perspective of goodness-of-fit, two tests statistics are proposed
for capturing different aspects of dynamic changes in the environmental.
It is found that the test that best embraces the concept of distribution
via the receiver operating characteristic (ROC) curve performs quite well. \par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Egg-distribution data, goodness-of-fit test, martingale central limit theory,
maximum likelihood approach, receiver operating characteristic (ROC) curve. \par
\end{quotation}

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